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Sleeping beauty and the dynamics of de se beliefs
Philosophical Studies 138 (2):245269 (2008)
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Darren Bradley has recently appealed to observation selection effects to argue that conditionalization presents no special problem for Everettian quantum mechanics, and to defend the ‘halfer’ answer to the puzzle of Sleeping Beauty. I assess Bradley’s arguments and conclude that while he is right about confirmation in Everettian quantum mechanics, he is wrong about Sleeping Beauty. This result is doubly good news for Everettians: they can endorse Bayesian confirmation theory without qualification, but they are not thereby compelled to adopt the (...) 

I show that centered propositions—also called de se propositions, and usually modeled as sets of centered worlds—pose a serious problem for various versions of Lewis's Principal Principle. The problem, put roughly, is that in scenarios like Elga's `Sleeping Beauty' case, those principles imply that rational agents ought to have obviously irrational credences. To solve the problem, I propose a centered version of the Principal Principle. My version allows centered propositions to be objectively chancy. 

The Snow White problem is introduced to demonstrate how learning something of which one could not have learnt the opposite can change an agent’s probability assignment. This helps us to analyse the Sleeping Beauty problem, which is deconstructed as a combinatorial engine and a subjective wrapper. The combinatorial engine of the problem is analogous to Bertrand’s boxes paradox and can be solved with standard probability theory. The subjective wrapper is clarified using the Snow White problem. Sample spaces for all three (...) 

The Mystery Room problem is a close variant of the Mystery Bag scenario. It is argued here that dealing with this problem requires no revision of the Bayesian formalism, since there exists a solution to this problem in which indexicals or demonstratives play no essential role. The solution does require labels, which are internal to the probabilistic model. While there needs to be a connection between at least one label and one indexical or demonstrative, that connection is external to the (...) 

Can selflocating beliefs be relevant to nonselflocating claims? Traditional Bayesian modeling techniques have trouble answering this question because their updating rule fails when applied to situations involving contextsensitivity. This essay develops a fully general framework for modeling stories involving contextsensitive claims. The key innovations are a revised conditionalization rule and a principle relating models of the same story with different modeling languages. The essay then applies the modeling framework to the Sleeping Beauty Problem, showing that when Beauty awakens her degree (...) 

The Sleeping Beauty Problem attracts so much attention because it connects to a wide variety of unresolved issues in formal epistemology, decision theory, and the philosophy of science. The problem raises unanswered questions concerning relative frequencies, objective chances, the relation between selflocating and nonselflocating information, the relation between selflocation and updating, Dutch Books, accuracy arguments, memory loss, indifference principles, the existence of multiple universes, and manyworlds interpretations of quantum mechanics. After stating the problem, this article surveys its connections to all (...) 

“Doublehalfers” think that throughout the Sleeping Beauty Problem, Beauty should keep her credence that a fair coin flip came up heads equal to 1/2. I introduce a new wrinkle to the problem that shows even doublehalfers can't keep Beauty's credences equal to the objective chances for all coinflip propositions. This leaves no way to deny that selflocating information generates an unexpected kind of inadmissible evidence. 

The Sleeping Beauty puzzle has dramatized the divisive question of how de se beliefs should be integrated into formal theories of rational belief change. In this paper, I look ahead to a related question: how should de se beliefs be integrated into formal theories of rational choice? I argue that standard decision theoretic frameworks fail in special cases of de se uncertainty, like Sleeping Beauty. The nature of the failure reveals that sometimes rational choices are determined independently of one’s credences (...) 

A longstanding issue in attempts to understand the Everett (ManyWorlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers are in a position of selflocating uncertainty during the period between the branches of the wave function splitting via decoherence and the observer registering the outcome of the measurement. In this period it is tempting to regard each branch as equiprobable, but we (...) 

How should rational beliefs change over time? The standard Bayesian answer is: by conditionalization (a.k.a. Bayes’ Rule). But conditionalization is not an adequate rule for updating beliefs in “centred” propositions whose truthvalue may itself change over time. In response, some have suggested that the objects of belief must be uncentred; others have suggested that beliefs in centred propositions are not subject to diachronic norms. Iargue that these views do not offer a satisfactory account of selflocating beliefs and their dynamics. A (...) 

I defend a general rule for updating beliefs that takes into account both the impact of new evidence and changes in the subject’s location. The rule combines standard conditioning with a shifting operation that moves the center of each doxastic possibility forward to the next point where information arrives. I show that wellknown arguments for conditioning lead to this combination when centered information is taken into account. I also discuss how my proposal relates to other recent proposals, what results it (...) 

When an agent undergoes fission, how should the beliefs of the fission results relate to the prefission beliefs? This question is important for the Everett interpretation of quantum mechanics, but it is of independent philosophical interest. Among other things, fission scenarios demonstrate that ‘selflocating’ information can affect the probability of uncentred propositions even if an agent has no essentially selflocating uncertainty. I present a general update rule for centred beliefs that gives sensible verdicts in cases of fission, without relying on (...) 

The aim of this paper is to apply the accuracy based approach to epistemology to the case of higher order evidence: evidence that bears on the rationality of one's beliefs. I proceed in two stages. First, I show that the accuracy based framework that is standardly used to motivate rational requirements supports steadfastness—a position according to which higher order evidence should have no impact on one's doxastic attitudes towards first order propositions. The argument for this will require a generalization of (...) 

Currently, the most popular views about how to update de se or selflocating beliefs entail the onethird solution to the Sleeping Beauty problem.2 Another widely held view is that an agent‘s credences should be countably additive.3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the onethird solution to the Sleeping Beauty problem entail a more general principle, which I call the Generalized Thirder Principle, and there are situations (...) 

Conditionalization is a norm that governs the rational reallocation of credence. I distinguish between factive and nonfactive formulations of Conditionalization. Factive formulations assume that the conditioning proposition is true. Nonfactive formulations allow that the conditioning proposition may be false. I argue that nonfactive formulations provide a better foundation for philosophical and scientific applications of Bayesian decision theory. I furthermore argue that previous formulations of Conditionalization, factive and nonfactive alike, have almost universally ignored, downplayed, or mishandled a crucial causal aspect of (...) 

One can have no prior credence whatsoever (not even zero) in a temporally indexical claim. This fact saves the principle of conditionalization from potential counterexample and undermines the Elga and Arntzenius/Dorr arguments for the thirder position and Lewis' argument for the halfer position on the Sleeping Beauty Problem, thereby supporting the doublehalfer position. / . 

Traditional procedures for rational updating fail when it comes to selflocating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with selflocating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information you have genuinely (...) 

The Sleeping Beauty problem has attracted considerable attention in the literature as a paradigmatic example of how selflocating uncertainty creates problems for the Bayesian principles of Conditionalization and Reflection. Furthermore, it is also thought to raise serious issues for diachronic Dutch Book arguments. I show that, contrary to what is commonly accepted, it is possible to represent the Sleeping Beauty problem within a standard Bayesian framework. Once the problem is correctly represented, the ‘thirder’ solution satisfies standard rationality principles, vindicating why (...) 

The Sleeping Beauty problem has attracted considerable attention in the literature as a paradigmatic example of how selflocating uncertainty creates problems for the Bayesian principles of Conditionalization and Reflection. Furthermore, it is also thought to raise serious issues for diachronic Dutch Book arguments. I show that, contrary to what is commonly accepted, it is possible to represent the Sleeping Beauty problem within a standard Bayesian framework. Once the problem is correctly represented, the ‘thirder’ solution satisfies standard rationality principles, vindicating why (...) 

Conditionalization is a widely endorsed rule for updating one’s beliefs. But a sea of complaints have been raised about it, including worries regarding how the rule handles error correction, changing desiderata of theory choice, evidence loss, selflocating beliefs, learning about new theories, and confirmation. In light of such worries, a number of authors have suggested replacing Conditionalization with a different rule — one that appeals to what I’ll call “urpriors”. But different authors have understood the rule in different ways, and (...) 

I argue that the theory of chance proposed by David Lewis has three problems: (i) it is time asymmetric in a manner incompatible with some of the chance theories of physics, (ii) it is incompatible with statistical mechanical chances, and (iii) the content of Lewis's Principal Principle depends on how admissibility is cashed out, but there is no agreement as to what admissible evidence should be. I proposes two modifications of Lewis's theory which resolve these difficulties. I conclude by tentatively (...) 

In this paper I show that Elga’s argument for a restricted principle of indifference for selflocating belief relies on the kind of mistaken reasoning that recommends the ‘staying’ strategy in the Monty Hall problem. 



Philosophy and Phenomenological Research, EarlyView. 

I give a Dutch book argument for CDT thirders in the context of a generalized Sleeping Beauty scenario. In combination with the Briggs (2010) Dutch book for EDT thirders, this amounts to a purely decisiontheoretic argument for halfing in Sleeping Beauty. In combination with the Hitchcock (2004) Dutch book for CDT halfers, this amounts to a Dutch book argument against CDT. The combined Dutch book against CDT invites a plausible diagnosis of the reasons for CDT’s failure: CDT is incompatible with (...) 

In his “Relevance of Selflocating Belief”, Titelbaum suggests a general theory about how to update one’s degrees of selflocating belief. He applies it to the Sleeping Beauty problem, more specifically, Lewis’s :171–176, 2001) version of that problem. By doing so, he defends the Thirder solution to the puzzle. Unfortunately, if we modify the puzzle very slightly, and if we apply his general updating theory to the thus modified version, we get the Halfer view as a result. In this paper, we (...) 

In this paper, I argue for a view largely favorable to the Thirder view: when Sleeping Beauty wakes up on Monday, her credence in the coin’s landing heads is less than 1/2. Let’s call this “the Lesser view.” For my argument, I (i) criticize Strict Conditionalization as the rule for changing de se credences; (ii) develop a new rule; and (iii) defend it by Gaifman’s Expert Principle. Finally, I defend the Lesser view by making use of this new rule. 

Many philosophers regard the imprecise credence framework as a more realistic model of probabilistic inferences with imperfect empirical information than the traditional precise credence framework. Hence, it is surprising that the literature lacks any discussion on how to update one’s imprecise credences when the given evidence itself is imprecise. To fill this gap, I consider two updating principles. Unfortunately, each of them faces a serious problem. The first updating principle, which I call “generalized conditionalization,” sometimes forces an agent to change (...) 

Is the fact that our universe contains finetuned life evidence that we live in a multiverse? Ian Hacking and Roger White influentially argue that it is not. We approach this question through a systematic framework for selflocating epistemology. As it turns out, leading approaches to selflocating evidence agree that the fact that our own universe contains finetuned life indeed confirms the existence of a multiverse. This convergence is no accident: we present two theorems showing that, in this setting, any updating (...) 

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of nonmeasurable sets. Nonmeasurable propositions cannot receive precise probabilities, but there is a natural (...) 

I advocate TimeSlice Rationality, the thesis that the relationship between two timeslices of the same person is not importantly different, for purposes of rational evaluation, from the relationship between timeslices of distinct persons. The locus of rationality, so to speak, is the timeslice rather than the temporally extended agent. This claim is motivated by consideration of puzzle cases for personal identity over time and by a very moderate form of internalism about rationality. TimeSlice Rationality conflicts with two proposed principles of (...) 

The best arguments for the 1/3 answer to the Sleeping Beauty problem all require that when Beauty awakes on Monday she should be uncertain what day it is. I argue that this claim should be rejected, thereby clearing the way to accept the 1/2 solution. 

In the Sleeping Beauty problem, Beauty is woken once if a coin lands heads or twice if the coin lands tails but promptly forgets each waking on returning to sleep. Philosophers have divided over whether her waking credence in heads should be a half or a third. Beauty has centered beliefs about her world and about her location in that world. When given new information about her location she should update her worldly beliefs before updating her locative beliefs. When she (...) 

The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle, would be that in the absence of new evidence the belief should not change. Yet, there are examples that are claimed to violate this assumption. The apparent paradox presented by such examples, if not settled, would demonstrate the inconsistency and/or incompleteness of the Bayesian approach, and (...) 



Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew, and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has been realized. I also argue that we should (...) 

Bayesianism is a collection of positions in several related fields, centered on the interpretation of probability as something like degree of belief, as contrasted with relative frequency, or objective chance. However, Bayesianism is far from a unified movement. Bayesians are divided about the nature of the probability functions they discuss; about the normative force of this probability function for ordinary and scientific reasoning and decision making; and about what relation (if any) holds between Bayesian and nonBayesian concepts. 

Among the most remarkable developments in metaphysics since the 1950’s is the explosion of philosophical interest in possible worlds. This paper proposes an explanation of what possible worlds are, and argues that this proposal, the interpreted models conception, should be attractive to anyone who thinks that modal facts are primitive, and so not to be explained in terms of some nonmodal notion of “possible world.” I articulate three constraints on any acceptable primitivist explanation of the nature of possible worlds, and (...) 

Recently, several epistemologists have defended an attractive principle of epistemic rationality, which we shall call UrPrior Conditionalization. In this essay, I ask whether we can justify this principle by appealing to the epistemic goal of accuracy. I argue that any such accuracybased argument will be in tension with Evidence Externalism, i.e., the view that agent's evidence may entail nontrivial propositions about the external world. This is because any such argument will crucially require the assumption that, independently of all empirical evidence, (...) 

The evolutionary argument is an argument against epiphenomenalism, designed to show that some mindbody theory that allows for the efficacy of qualia is true. First developed by Herbert Spencer and William James, the argument has gone through numerous incarnations and it has been criticized in a number of different ways. Yet many have found the criticisms of the argument in the literature unconvincing. Bearing this in mind, I examine two primary issues: first, whether the alleged insights employed in traditional versions (...) 

In the context of the Sleeping Beauty problem, it has been argued that socalled “halfers” can avoid Dutch book arguments by adopting evidential decision theory. I introduce a Dutch book for a variant of the Sleeping Beauty problem and argue that evidential decision theorists fall prey to it, whether they are halfers or thirders. The argument crucially requires that an action can provide evidence for what the agent would do not only at other decision points where she has exactly the (...) 

How should we update de dicto beliefs in the face of de se evidence? The Sleeping Beauty problem divides philosophers into two camps, halfers and thirders. But there is some disagreement among halfers about how their position should generalize to other examples. A full generalization is not always given; one notable exception is the Halfer Rule, under which the agent updates her uncentered beliefs based on only the uncentered part of her evidence. In this brief article, I provide a simple (...) 

Analyses of the Sleeping Beauty Problem are polarised between those advocating the “1/2 view” and those endorsing the “1/3 view”. The disagreement concerns the evidential relevance of selflocating information. Unlike halfers, thirders regard selflocating information as evidentially relevant in the Sleeping Beauty Problem. In the present study, we systematically manipulate the kind of information available in different formulations of the Sleeping Beauty Problem. Our findings indicate that patterns of judgment on different formulations of the Sleeping Beauty Problem do not fit (...) 

The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for selflocating beliefs or centered propositions. (...) 

Supersubstantivalism, the view that material objects are identical to their locations, has recently been defended in metaphysics and philosophy of physics. One of the most powerful arguments in its favour is the socalled argument from harmony. There is a certain harmony between material objects and their locations. Necessarily, if material object x is located at a spherical region, x is spherical. Necessarily, if material object x is located at region r, any part of x is located at a part of (...) 



In this paper, I argue that some plausible principles concerning which credences are rationally permissible for agents given information about one another’s epistemic and credal states have some surprising consequences for which credences an agent ought to have in light of selflocating information. I provide a framework that allows us to state these constraints and draw out these consequences precisely. I then consider and assess the prospects for rejecting these prima facie plausible principles. 

The epistemology of selflocating belief concerns itself with how rational agents ought to respond to certain kinds of indexical information. I argue that those who endorse the thesis of TimeSlice Rationality ought to endorse a particular view about the epistemology of selflocating belief, according to which ‘essentially indexical’ information is never evidentially relevant to nonindexical matters. I close by offering some independent motivations for endorsing TimeSlice Rationality in the context of the epistemology of selflocating belief. 

I argue that different views in the metaphysics of time make different observational predictions in both classical and relativistic cases. Because different views in the metaphysics of time differ over which facts are merely indexical facts, they make different observational predictions about certain selflocating propositions. I argue for this thesis by distinguishing the three main updating procedures that apply in cases of selflocating uncertainty, and I present a series of cases which cumulatively show that every one of these updating procedures (...) 